On the phone, it keeps giving me options for weather for Ny and A city about 60 miles away from me and rarely the area that I am in. How do I get rid of the former. How do I fix the latter so it is actually for my city?
Turn on Google location services. It's the only one required and the only one the weather app seems to use..you'll find the setting: settings>location.
While in the Weather app, select the Menu button, then Edit. The list of locations should come up. Just check the location(s) you want to remove (a red X should appear indicating a Delete) and then click Done.